For learning, without loss of generality, we adopt FedAvg [1]} to solve problem (REF ). At each global iteration \(t\) , the BS randomly selects a set of devices \(\mathcal {N}_t\)  with \(|\mathcal {N}_t| = K\)  and broadcasts the current global model \(w_t\)  to the scheduled devices. Each device in \(\mathcal {N}_t\)  trains its local model based on the received global model by running \(I\)  steps of SGD on its local loss function as below
\(w_{t, \tau }^k \hspace{-1.42262pt}= \hspace{-1.42262pt} w_{t, \tau -1}^k \hspace{-1.42262pt}- \hspace{-1.42262pt} \eta _t \nabla F_k(w^{Q, k}_{t, \tau -1}, \xi ^k_\tau ), \forall \tau \hspace{-1.42262pt} = \hspace{-1.42262pt} 1, \dots , I, \) 
